theorem Th59: :: CHORD:60

for G being _Graph
for S being non empty Subset of (the_Vertices_of G)
for H being inducedSubgraph of G,S
for u being Vertex of G st u in S & G .AdjacentSet {u} c= S & G .AdjacentSet {u} <> {} holds
for v being Vertex of H st u = v holds
for Ga being AdjGraph of G,{u}
for Ha being AdjGraph of H,{v} holds Ga == Ha